QUIZ (1425)
Materi: Matriks
Berapakah nilai determinan matriks [tex] \displaystyle \left[\begin{matrix}1&4&2\\5&-1&-4\\-2&-5&9\\\end{matrix}\right] [/tex] ?
Materi: Matriks
Berapakah nilai determinan matriks [tex] \displaystyle \left[\begin{matrix}1&4&2\\5&-1&-4\\-2&-5&9\\\end{matrix}\right] [/tex] ?
Verified answer
Jawaban:
Matriks
Determinan
Penjelasan dengan langkah-langkah:
Aturan Sarrus
- - - ( kiri bawah ke kanan atas )
[ 1 4 2][ 1. 4 ]
[ 5 -1. -4][ 5 -1 ]
[ -2 -5 9][-2 -5]
+ + + ( kiri atas ke kanan bawah )
= [(1)(-1)(9)+(4)(-4)(-2)+(2)(5)(-5)-(-2)(-1)(2)-(-5)(-4)(1)-(9)(5)(4)]
= [(-9+32-50-4-20-180)]
= [(23-54-200)]
= [(-31-200)]
= [(-231)]
Demikian
-231
Penjelasan dengan langkah-langkah:
[tex]\displaystyle\tt~ \displaystyle \left[\begin{matrix}1&4&2\\5&-1&-4\\-2&-5&9\\\end{matrix}\right] = \displaystyle\tt~ \displaystyle \left[\begin{matrix}a&b&c\\d&e&f\\g&h&i\\\end{matrix}\right][/tex]
[tex]\begin{aligned} \displaystyle\tt~Determinan & = \displaystyle\tt~aei + bfg + cdh - ceg - afh - bdi \\ & = \displaystyle\tt~(1)( - 1)(9) + (4)( - 4)( - 2) + (2)(5)( - 5) - (2)( - 1)( - 2) - (1)( - 4)( - 5) - (4)(5)(9) \\ & = \displaystyle\tt~ - 9 + 32 - 50 - 4 - 20 - 180 \\ & = \displaystyle\tt~ - 231 \end{aligned}[/tex]